Question

Three unbiased coins are tossed together. Find the probability of getting:
(a) All heads

(b) Two heads

(c) Atmost two heads

(d) Getting a head and tail alternately​

Answer 1

Answer:-

a.1/8

b: 3/8

c: 7/8

Step-by-step explanation:

S:- (TTT, TTH, THT, THH, HTT, HTH, HHT, HHH)

NOW ACC. TO EVENTS DECIDE PROBABILITY

(a). all heads:- (HHH)

(b). two heads:- (THH,HTH,HHT)

(c) atmost two heads :- all except HHH

Answer 2

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Answer: i) 3/8 ,  ii) 3/8 , iii) 1/2

Step-by-step explanation:  

Sample  space  of  tossing 3 coins together (Set  of total possible  events know  as  sample space)

S = {HHH , HHT , HTH , THH , TTH , THT , HTT , TTT }

n(S) = 8

i) One head

Events  having  one head,

E = {TTH , THT , HTT}

n(E) = 3

Hence,

Probability of  getting one head = n(E)/n(S) = 3/8

ii)Two heads

Events  having  two head,

E = {THH ,HHT , HTH}

n(E) = 3

Hence,

Probability of  getting one head = n(E)/n(S) = 3/8

(iii) All heads

Events  having  all heads,

E = {HHH}

n(E) = 1

Hence,

Probability of  getting one head = n(E)/n(S) = 1/8

(iv) at least two heads:- It means that at  heads two heads or  more that two as more as possible.

Events  having at least two heads,

E = {HHT, HHT , HTH , HHH}

n(E) = 4

Hence,

Probability of  getting one head = n(E)/n(S) = 4/8 = 1/2